标题： 高频率金融数据的大型即时波动率矩阵的非参数估计 显示英文标题

标题： Nonparametric Estimation of Large Spot Volatility Matrices for High-Frequency Financial Data

摘要： 在本文中，我们考虑估计高频率数据的即时波动率矩阵，这些数据是针对大量资产收集的。 我们首先将经典的非参数核平滑方法与矩阵估计中的广义收缩技术相结合，在均匀稀疏性假设下对无噪声数据进行估计，这是文献中常用近似稀疏性的自然扩展。 所提出的即时波动率矩阵估计量具有统一一致性的性质，其收敛速度与最优最小最大速度相当。 对于受到微观结构噪声污染的高频数据，我们引入了一种局部预平均估计方法，以降低噪声的有效幅度。 然后，我们使用无噪声情况下开发的估计工具，并推导出所开发的即时波动率矩阵估计量的统一收敛速度。 我们进一步将核平滑与收缩技术结合，以估计高维噪声向量的时间变化波动率矩阵。 此外，我们考虑了具有可观测风险因素的时间变化因子模型中的大即时波动率矩阵估计，并推导出统一收敛性质。 我们提供了包括模拟和实证应用在内的数值研究，以检验所提出的估计方法在有限样本中的性能。 显示英文摘要

摘要： In this paper, we consider estimating spot/instantaneous volatility matrices of high-frequency data collected for a large number of assets. We first combine classic nonparametric kernel-based smoothing with a generalised shrinkage technique in the matrix estimation for noise-free data under a uniform sparsity assumption, a natural extension of the approximate sparsity commonly used in the literature. The uniform consistency property is derived for the proposed spot volatility matrix estimator with convergence rates comparable to the optimal minimax one. For the high-frequency data contaminated by microstructure noise, we introduce a localised pre-averaging estimation method that reduces the effective magnitude of the noise. We then use the estimation tool developed in the noise-free scenario, and derive the uniform convergence rates for the developed spot volatility matrix estimator. We further combine the kernel smoothing with the shrinkage technique to estimate the time-varying volatility matrix of the high-dimensional noise vector. In addition, we consider large spot volatility matrix estimation in time-varying factor models with observable risk factors and derive the uniform convergence property. We provide numerical studies including simulation and empirical application to examine the performance of the proposed estimation methods in finite samples.